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        <article id="post-Java-数学运算"
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  	<a href="/2019/01/11/Java-数学运算/">
    	Java 数学运算
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	  Jan 11, 2019
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	</section>
	
		<section class="toc-wrapper"><ol class="toc"><li class="toc-item toc-level-3"><a class="toc-link" href="#Math-类"><span class="toc-number">1.</span> <span class="toc-text">Math 类</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#常用数学运算方法"><span class="toc-number">2.</span> <span class="toc-text">常用数学运算方法</span></a></li></ol></section>
	
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    	<p>在 Java 语言中提供了一个执行数学基本运算的 Math 类，该类包括常用的数学运算方法，如三角函数方法、指数函数方法、对数函数方法、平方根函数方法等一些常用数学函数，初次之外还提供了一些常用的数学常量，如PI、E等。</p>
<h3 id="Math-类"><a href="#Math-类" class="headerlink" title="Math 类"></a>Math 类</h3><p>在 Math 类中提供了众多数学函数方法，主要包括三角函数方法、指数函数方法、取整函数方法、取最大值、最小值和平均值函数方法，这些方法都被定义成 static 形式，方便调用。</p>
<h3 id="常用数学运算方法"><a href="#常用数学运算方法" class="headerlink" title="常用数学运算方法"></a>常用数学运算方法</h3><p>在 Math 类中的常用数学运算方法较多，大致可以将其分为 4 大类别。分别为 三角函数方法、指数函数方法、取整函数方法以及取最大值、最小值好绝对值函数方法。</p>
<ol>
<li>三角函数方法<br>在 Math 类中包含的三角函数方法如下：<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">sin</span><span class="params">(<span class="keyword">double</span> a)</span></span>; 返回角的三角正弦</span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">cos</span><span class="params">(<span class="keyword">double</span> a)</span></span>; 返回角的三角余弦</span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">tan</span><span class="params">(<span class="keyword">double</span> a)</span></span>; 返回角的三角正切</span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">asin</span><span class="params">(<span class="keyword">double</span> a)</span></span>; 返回一个值的反正弦</span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">acos</span><span class="params">(<span class="keyword">double</span> a)</span></span>; 返回一个值的反余弦</span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">atan</span><span class="params">(<span class="keyword">double</span> a)</span></span>; 返回一个值的反正切</span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">toRadians</span><span class="params">(<span class="keyword">double</span> angdeg)</span></span>; 将角度转换为弧度</span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">toDegrees</span><span class="params">(<span class="keyword">double</span> angrad)</span></span>; 将弧度转换为角度</span><br></pre></td></tr></table></figure>
</li>
</ol>
<p><strong>特别注意的是：角度和弧度转换通常是不精确地</strong></p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">TrigonometricFunction</span></span>&#123;</span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">main</span><span class="params">(String args)</span> </span>&#123;</span><br><span class="line">        <span class="comment">//取 90 °的正弦</span></span><br><span class="line">        System.out.println(<span class="string">"90度的正弦值："</span>+Math.sin(Math.PI/<span class="number">2</span>))；</span><br><span class="line">        <span class="comment">//取 0 ° 的余弦</span></span><br><span class="line">        System.out.println(<span class="string">"0度的余弦值："</span>+Math.cos(<span class="number">0</span>));</span><br><span class="line">        <span class="comment">//取 60 ° 的 正切</span></span><br><span class="line">        System.out.println(<span class="string">"60 度的正切值:"</span> + Math.tan(Math.PI / <span class="number">3</span>));</span><br><span class="line">        </span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<ol start="2">
<li>指数函数方法</li>
</ol>
<p>Math 类中与指数相关的函数方法如下：<br><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">exp</span><span class="params">(<span class="keyword">double</span> a)</span></span>; <span class="comment">//用于获取 e 的 a 次方</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">log</span><span class="params">(<span class="keyword">double</span> a)</span></span>; <span class="comment">//用于取自然对数</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">log10</span><span class="params">(<span class="keyword">double</span> a )</span></span>; <span class="comment">//用于取底数为10的对数</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">sqrt</span><span class="params">(<span class="keyword">double</span> a )</span></span>;<span class="comment">//用于取 a 的平方根，其中 a 不能为负值</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">cbrt</span><span class="params">(<span class="keyword">double</span> a )</span></span>;   <span class="comment">//用于取 a 的立方根</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">pow</span><span class="params">(<span class="keyword">double</span> a, <span class="keyword">double</span> b)</span></span>;<span class="comment">//用于取  a 的 b 次方</span></span><br></pre></td></tr></table></figure></p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">ExponentFunction</span></span>&#123;</span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">main</span><span class="params">(String[] args)</span> </span>&#123;</span><br><span class="line">        System.out.println(<span class="string">"e 的平方值："</span> + Math.exp(<span class="number">2</span>));</span><br><span class="line">        <span class="comment">//取以 e 为底 2 的对数</span></span><br><span class="line">        System.out.println(<span class="string">"以e为底2的对数："</span>+ Math.log(<span class="number">2</span>));</span><br><span class="line">        <span class="comment">//取以10 为底 2 的对数</span></span><br><span class="line">        System.out.println(<span class="string">"以10为底 2 的对数值："</span>+Math.log10(<span class="number">2</span>));</span><br><span class="line">        System.out.println(<span class="string">"4 的平方根值："</span> + Math.sqrt(<span class="number">4</span>));</span><br><span class="line">        System.out.println(<span class="string">"8 的立方根值："</span>+Math.cbrt(<span class="number">8</span>));</span><br><span class="line">        System.out.println(<span class="string">"2 的 2 次方值："</span> + Math.pow(<span class="number">2</span>,<span class="number">2</span>));</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<ol start="3">
<li>取整函数方法<br>在具体的问题中，取整操作使用也很普遍。<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">ceil</span><span class="params">(<span class="keyword">double</span> a)</span></span>;<span class="comment">//返回大于等于参数的最小整数 </span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">floor</span><span class="params">(<span class="keyword">double</span> a)</span></span>;   <span class="comment">//返回小于等于参数的最大整数</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">rint</span><span class="params">(<span class="keyword">double</span> a)</span></span>;<span class="comment">//返回与参数最接近的整数，如果两个同为整数且童颜接近，则结果取整数、</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">int</span> <span class="title">round</span><span class="params">(<span class="keyword">float</span> a)</span></span>;<span class="comment">//将参数加上0.5后返回与参数最近的整数</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">long</span> <span class="title">round</span><span class="params">(<span class="keyword">double</span> a )</span></span>;<span class="comment">//将参数加上0.5之后返回与参数最近的整数，然后强制转换为长整型</span></span><br></pre></td></tr></table></figure>
</li>
</ol>
<p><strong>由于数 1.0和 数 2.0 距离数 1.5 都是0.5个单位长度，因此返回偶数 2.0</strong><br><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">intFunction</span></span>&#123;</span><br><span class="line">    <span class="comment">//返回第一个大于等于参数的整数</span></span><br><span class="line">    System.out.println(<span class="string">"使用 ceil() 方法取整："</span>+Math.ceil(<span class="number">5.2</span>));</span><br><span class="line">    <span class="comment">//返回第一个小于等于参数的整数</span></span><br><span class="line">    System.out.println(<span class="string">"使用 floor 方法取整："</span>+ Math.floor(<span class="number">2.5</span>));</span><br><span class="line">    <span class="comment">//返回与参数最接近的整数</span></span><br><span class="line">    System.out.println(<span class="string">"使用 rint() 方法取整："</span>+Math.rint(<span class="number">2.7</span>));</span><br><span class="line">    <span class="comment">//返回与参数最接近的整数</span></span><br><span class="line">    System.out.println(<span class="string">"使用 rint 方法取整："</span>+ Math.rint(<span class="number">2.5</span>));</span><br><span class="line">    <span class="comment">//将参数加上 0.5 之后返回最接近的整数</span></span><br><span class="line">    System.out.println(使用 round方法取整：<span class="string">"+Math.round(3.4f));</span></span><br><span class="line"><span class="string">    //将参数加上 0.5 之后返回最接近的整数，并将结果强制转换为长整型</span></span><br><span class="line"><span class="string">    System.out.println("</span>使用 round 方法取整：<span class="string">"+Math.round(2.5));</span></span><br><span class="line"><span class="string"></span></span><br><span class="line"><span class="string">&#125;</span></span><br></pre></td></tr></table></figure></p>
<ol start="4">
<li>取最大值、最小值、绝对值函数方法</li>
</ol>
<p>在程序中最常用的方法就是取最大值、最小值、绝对值等，在 Math 类中包括这些操作方法<br><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">max</span><span class="params">(<span class="keyword">double</span> a, <span class="keyword">double</span> b)</span></span>;<span class="comment">//取a与b之间的最大值</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">int</span> <span class="title">min</span><span class="params">(<span class="keyword">int</span> a, <span class="keyword">int</span> b)</span></span>;<span class="comment">//取a与b之间的最小值，参数是整型</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">long</span> <span class="title">min</span><span class="params">(<span class="keyword">long</span> a, <span class="keyword">long</span> b)</span></span>;<span class="comment">//取a与b之间的最小值，参数是长整型</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">float</span> <span class="title">min</span><span class="params">(<span class="keyword">float</span> a, <span class="keyword">float</span> b)</span></span>;<span class="comment">//取a与b之间的最小值，参数是浮点型</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">min</span><span class="params">(duble a, <span class="keyword">double</span> b)</span></span>;<span class="comment">//取a与b之间的最小值，参数是双精度型</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">int</span> <span class="title">abs</span><span class="params">(<span class="keyword">int</span> a)</span></span>;<span class="comment">//返回整形参数的绝对值</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">long</span> <span class="title">abs</span><span class="params">(<span class="keyword">long</span> a)</span></span>;<span class="comment">//返回长整型参数的绝对值</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">float</span> <span class="title">abs</span><span class="params">(<span class="keyword">float</span> a)</span></span>;<span class="comment">//返回浮点型参数的绝对值</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">double</span> <span class="title">abs</span><span class="params">(<span class="keyword">double</span> a)</span></span>;<span class="comment">//返回双精度型参数的绝对值</span></span><br></pre></td></tr></table></figure></p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">AnyFunction</span></span>&#123;</span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">main</span><span class="params">(String[] args)</span> </span>&#123;</span><br><span class="line">        System.out.println(<span class="string">"4 和 8 较大者："</span>+ Math.max(<span class="number">4</span>,<span class="number">8</span>));</span><br><span class="line">        <span class="comment">//取两个参数的最小值</span></span><br><span class="line">        System.out.println(<span class="string">"4.4 和 4 较小者："</span>+Math.min(<span class="number">4.4</span>, <span class="number">4</span>));</span><br><span class="line">        <span class="comment">//取参数的绝对值</span></span><br><span class="line">        System.out.println(<span class="string">"-7 的绝对值："</span>+ Math.abs(-<span class="number">7</span>));</span><br><span class="line">    </span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
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